The study proves a quantitative functional CLT for neural networks with smooth activation functions.
problem Understanding the convergence rates of neural networks with different activation functions.
method Functional versions of the Stein-Malliavin approach and a quantitative functional central limit theorem.
result Rates of convergence depend on the smoothness of the activation function, ranging from logarithmic to sqrt(n).
Alpha-GPT 2.0 integrates human insights into AI-driven investment research.
problem Efficiency and precision in quantitative investment research.
method Iterative Human-AI interaction using large language models.
result Enhanced efficiency and precision in quantitative investment research.
Alternative approach to rigidity of high-dimensional isometric immersions.
problem Rigidity of high-dimensional isometric immersions between compact manifolds.
method Quantitative rigidity estimates, reducing to Euclidean setting and applying Friesecke-James-Müller rigidity estimate.
result Quantitative results showing close proximity to isometric immersions for small stretching and bending energy.
Study proves quantitative results for isoperimetric problem outside convex bodies in the plane.
problem Quantitative estimates for the relative isoperimetric problem outside convex bodies in the plane.
method Flow approach and Łojasiewicz estimates to prove quantitative stability for minimizers.
result Explicit constants and optimal exponents/rates for Łojasiewicz estimates and rates of convergence for gradient flow.
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
problem Voxel independence assumption limits model fitting reliability and repeatability.
method Self-supervised deep variational approach with Gaussian mixture prior.
result Our method outperforms current techniques in dMRI simulations and real data.
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some r…
QuantBench benchmarks AI methods for quantitative investment.
problem Lack of a standardized benchmark for AI in quantitative investment.
method Developed an industrial-grade benchmark platform with standardization, flexibility, and full-pipeline coverage.
result Revealed critical research directions in AI for quantitative investment.
Researchers create integral representations for two-layer ReLU networks with quantitative bounds.
problem Approximating functions with two-layer ReLU networks using explicit integral representations.
method Developed integral representations involving harmonic extension and projection, providing L2 bounds. result Functions can be approximated with L2 errors independent of dimension or degree, depending on coefficients and distribution. Research integrates sentiment analysis with reinforcement learning for better trading strategies.
problem Improving trading performance by integrating sentiment data.
method Developed a sentiment-driven trading system using a large language model and reinforcement learning.
result Sentiment signals from FinGPT improve trading performance when combined with technical indicators.
Analyzes quantitative finance papers from arXiv using text mining and NLP.
problem Understanding trends and insights in quantitative finance research.
method Text mining, natural language processing, topic modeling.
result Identified most cited researchers and journals in quantitative finance.
The purpose of this research paper it is to present a new approach in the framework of a biased roulette wheel. It is used the approach of a quantitative trading strategy, commonly used in quantitative finance, in order to assess the profitability of the strategy in the short term. The tools of backtesting and walk-for…
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
Quantitative model predicts Sri Lankan stock market using NLP, clustering, and time-series forecasting.
problem Predicting economic regimes and market signals in Sri Lankan stock indices.
method Integrates NLP, clustering, and time-series forecasting; uses FinBERT for sentiment analysis, UMAP/HDBSCAN for clustering, and GRU/LSTM for forecasting.
result GRU model achieves 80.1% R-squared for daily closing price forecasts.
We prove the following quantitative version of the celebrated Soap Bubble Theorem of Alexandrov. Let S be a C2 closed embedded hypersurface of Rn+1, n≥1, and denote by osc(H) the oscillation of its mean curvature. We prove that there exists a positive ε, depending on n and upper …
Paper proposes a new approach to GDPR compliance using data protection analytics.
problem Lack of research on data protection risk management and difficulty in GDPR compliance.
method Quantitative approach to data protection risk-based compliance.
result Improves data protection impact assessments by integrating analytics and expert opinions.
The Alexandrov Soap Bubble Theorem asserts that the distance spheres are the only embedded closed connected hypersurfaces in space forms having constant mean curvature. The theorem can be extended to more general functions of the principal curvatures f(k1,…,kn−1) satisfying suitable conditions. In this paper…
Qlib aims to integrate AI into quantitative investment.
problem Challenges in applying AI to quantitative investment.
method Design and develop Qlib to accommodate AI-driven workflow.
result Qlib realizes the potential of AI technologies in quantitative investment.
Framework uses LLMs to automate strategy finding in quantitative finance.
problem Brittleness of traditional deep learning models in financial applications.
method Three-stage framework with prompt-engineered LLMs, multimodal agent-based evaluation, and dynamic weight optimization.
result Robust performance in Chinese & US markets, superior risk-adjusted performance.
This paper explores how combining quantitative factors and news from LLMs improves stock return prediction.
problem Improving stock return prediction using quantitative factors and news.
method Introduces a fusion learning framework to learn unified representations from factors and LLM-generated newsflow, comparing combination, summation, and attentive methods. Explores mixture models and decoupled training approaches.
result Effective multimodal modeling of factors and news improves stock return prediction and selection.
Optimizes PnL using linear signals in quantitative finance.
problem Maximizing profit and loss in financial trading.
method Unsupervised machine learning approach that maximizes Sharpe Ratio through linear relationships and parameter optimization.
result Empirical validation and effectiveness of the model on U.S. Treasury ETF.
The book explores essential stats and psychology for quantitative trading.
problem Developing a quantitative trading system.
method Logical progression through articles on statistics, quantitative trading, and psychology.
result Essential elements for quantitative trading systems.
Although Bayesian Optimization (BO) has been employed for accelerating materials design in computational materials engineering, existing works are restricted to problems with quantitative variables. However, real designs of materials systems involve both qualitative and quantitative design variables representing materi…
Which topics of machine learning are most commonly addressed in research? This question was initially answered in 2007 by doing a qualitative survey among distinguished researchers. In our study, we revisit this question from a quantitative perspective. Concretely, we collect 54K abstracts of papers published between 2…
Proves quantitative Alexandrov theorem for capillary surfaces.
problem Proving a quantitative version of the Alexandrov theorem for capillary hypersurfaces.
method Quantitative analysis of Montiel-Ros-type argument.
result Generalizes Julin-Niinikoski's result to capillary case.
Unified view of SOMs and SNE from a common framework.
problem Comparing and understanding SOMs and SNE.
method Unified mathematical framework, quantitative comparison on datasets.
result SOMs and SNE can be derived from a common framework.
We provide sharp stability estimates for the Alexandrov Soap Bubble Theorem in the hyperbolic space. The closeness to a single sphere is quantified in terms of the dimension, the measure of the hypersurface and the radius of the touching ball condition. As consequence we obtain a new pinching result for hypersurfaces i…
Proves upper bound on filling radius for manifolds with positive scalar curvature.
problem Bounding the filling radius of manifolds with positive scalar curvature.
method Quantitative operator K-theory and index theory.
result Proves a quantitative upper bound on the filling radius.
The paper develops quantitative estimates for holomorphic sections over bounded domains.
problem Establishing precise inequalities for holomorphic sections over bounded domains.
method Develops Sobolev-type inequalities and applies them to holomorphic sections of Hermitian vector bundles.
result Quantitative Carleman-type estimates for holomorphic sections are derived, improving on previous non-quantitative results.
This research develops a dynamic risk management system for industrial companies.
problem Risk assessment and management in industrial enterprises.
method Qualitative and quantitative analysis, systematic risk classification, dynamic system development.
result Effective risk management strategies formed through dynamic risk management system and risk assessment methods.
Pre-trained LLM adapted with LoRA improves offline RL for quantitative trading.
problem Challenges in offline RL for quantitative trading due to complex temporal dependencies and overfitting.
method Integrates pre-trained GPT-2 weights and LoRA for efficient fine-tuning of a Decision Transformer.
result Outperforms existing offline RL methods in certain trading scenarios.
Develops connections between operator K-theory and positive scalar curvature.
problem Positive scalar curvature on closed spin manifolds and Gromov's band width conjecture.
method Quantitative index theory and related techniques.
result The propagation of the index of the Dirac operator is inversely related to the curvature lower bound.
Sig-SDE model integrates signatures with SDEs for financial data.
problem Calibrating models to exotic financial products with non-linear dependencies.
method Integrating signatures from stochastic analysis with neural SDEs.
result Sig-SDE provides theoretical guarantees for convergence.
AI enhances quantitative investment for better returns and risk control.
problem Achieving stable returns through AI in quantitative investment.
method Application of AI technology in quantitative investment strategies.
result AI improves investment performance and risk management.
We outline the idiosyncrasies of neural information processing and machine learning in quantitative finance. We also present some of the approaches we take towards solving the fundamental challenges we face.
This paper presents quantitative shrinking target results for rotations and interval exchange transformations. To do this a quantitative version of a unique ergodicity criterion of Boshernitzan is established.
We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined s…
EQD model improves domain-specific QA by 0.6% to 10.5%.
problem Challenges in domain-specific quantitative reasoning for LLMs.
method Two-step fine-tuning framework guided by a reward function.
result EQD outperforms state-of-the-art models and prompting strategies.
Quantum neural networks can approximate noisy functions accurately.
problem Approximating noisy functions with quantum neural networks.
method Universal approximation theorem with error bounds for noisy quantum neural networks.
result Quantum neural networks can approximate noisy functions with precise error bounds.
Study connects manifold complexity to scalar curvature bounds.
problem Understanding the relationship between manifold complexity and scalar curvature.
method Combining quantitative operator K-theory, Lipschitz topological K-theory, and a vanishing theorem.
result Established a relationship between covering complexity and scalar curvature bounds.
Study shows how close functions are to optimal in Riemannian manifolds.
problem Understanding how close functions are to optimal in Riemannian manifolds.
method Analyzes quantitative stability of Sobolev inequalities on compact Riemannian manifolds.
result Functions that nearly saturate a critical Sobolev inequality are quantitatively close to extremal functions.
Quantitative estimate for curvature in mean curvature flow.
problem Estimating curvature in mean curvature flow.
method Proving a curvature estimate for smooth convex ancient flows.
result Curvature grows at most quadratically in terms of rescaled extrinsic distance.
Study evaluates LLMs for predicting Chinese stock movements using financial news sentiments.
problem Evaluating LLMs' ability to predict stock price movements using financial news sentiments.
method Standardized experimental procedure with three LLMs, each with unique performance enhancement methods.
result Developed quantitative trading strategies and conducted back-tests to assess LLMs' performance.
Quantitative Sobolev extensions lead to Neumann heat kernel bounds.
problem Bounding Neumann heat kernels for domains with integral Ricci curvature.
method Quantitative Sobolev extension operators and Neumann heat kernel estimates.
result Uniform bounds on Neumann heat kernels and eigenvalues.
Quantitative stability for nearly minimizing Yamabe metrics.
problem Understanding the stability of nearly minimizing metrics in Riemannian geometry.
method Proving quantitative closeness of nearly minimizing metrics to minimizing metrics in a specific sense.
result The distance between nearly minimizing metrics and minimizing metrics is controlled quadratically by the Yamabe energy deficit.
Survey of AI in quant finance, from deep learning to LLMs.
problem Improving predictive modeling and automation in asset management.
method Exploring AI contributions to quant investment pipeline, from human-crafted features to LLMs.
result AI has enabled scalable modeling and autonomous agents in quant finance.
Quantitative rigidity theorem for Alexandrov spaces with curvature bounds.
problem Quantifying rigidity in Alexandrov spaces with curvature constraints.
method Using Gromov-Hausdorff distance and properties of Alexandrov spaces.
result Alexandrov spaces with curvature bounds are close to hyperbolic manifolds.
In this paper, we present a novel approach to the generation of virtual scenarios of multivariate financial data of arbitrary length and composition of assets. With this approach, decades of realistic time-synchronized data can be simulated for a large number of assets, producing diverse scenarios to test and improve q…
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.